53 1 




RiCAL DRAWING 



COLLECTION or PUTtS 
FOR PRACTICAL USE IN 



ELEMENTARY 

MECHANICAL DRAW! 




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F. Schraidt. 



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Class ^i^ tl^i-^ 

Book O S _. 
Copyright}^" 



COPYRIGHT DEPOSIR 



GEOMETRICAL DRAWING 

A Collection of Plates for Practical Use in 

ELEMENTARY MECHANICAL DRAWING 



BY 

F. SCHRAIDT, M. A. 

Head of the Department of Drawing, Oakland High School 

OAKLAND, CALIFORNIA 




19 15 
PUBLISHERS 

WHITAKER AND RAY-WIGGIN CO. 

San Francisco 







Copyrighted 1915 by 




WHITAKER & RAY-WIGGIN CO. 




AiJG 2j 1915 




/^./^ 





CONTENTS 


. . V 


Introduction 


List of Drawing Equipment . 
Explanatory Notes 

PrATFS . 


. . VI 

. . VII 
. . 1-65 


Geometrical Data 


. . 66 



INTRODUCTION 

Geometrical Drawing (Elementarj' Mechanical Drawing) as a school subject comprises a 
two-fold purpose: a pedagogical and a purely practical one. A pedagogical benefit lies in the 
training in regard to the pupil's accuracy and definiteness. The object is not merely to rep- 
resent geometrical figures by a set of lines, but these lines must be closely observed, accurately 
measured and definitely placed. This feature of discipline must always be kept in mind. The 
plate of Geometrical Drawing is also to develop an active sense for symmetry and harmony; the 
different figures and problems should be placed so as to balance the whole outline. The general 
impression of the finished drawing should be one of neatness, expressed in line-work and letter- 
ing, and of cleanliness. 

While this purely pedagogical benefit is alwaj's evident. Geometrical Drawing is particu- 
larly valuable as Elementary Mechanical Drawing for vocational work, be it for mechanical 
or structural or architectural engineering. Not only that Geometry and the "French" Curve 
as such form a necessary schooling for the professional draftsman and engineer, but the student 
becomes acquainted in this work with his mechanical appliances, as scale, T-square, triangles, 
compass, ruling pen, brush, etc. and learns their proper use. With this knowledge he is prepared 
to handle more difficult problems of drawing since he has previously acquired a critical eye and 
a trained hand. 

Here it should be remembered, that the nature of this preparatory drawing in regard to the 
choice of its problems is not so important as the exactness in the line-work itself. A student, who 
has acquired a sense for accuracy and habitual neatness is well prepared for his professional 
work because he has learned the one important prerequisite, namely : how to make any drawing 
intelligent and reliable. 



VI 



LIST OF DRAWING EQUIPMENT 

(A SUGGESTION) 



1. One Drawing Board, about 16" x 22". 

2. One 24" T-Square, maple blade, walnut 

fixed head, 
or Transparent Edges. 

3. One 30° Triangle, about 10", Transparent. 

4. One 45° Triangle, about 8", Transparent. 

5. One Triangular Boxwood Architect Scale, 

12". 

6. One Set of Instruments, consisting of 

One 6" Compass with Pen and Pencil 

Attachment. 
One 6" Dividers. 
One Sy." Pen Bow. 
One 5" Ruling Pen. 



7. Two Sheets of Cream colored Drawing 

Paper, 27" x 40". . 
This size of paper will furnish 4 plates 
each. If good quality ("Duplex" or 
"Corona") is selected, it will take ink 
well, while its cream color does not 
strain the eye as much as the glaring 
white. 

8. One A. W. Faber Drawing Pencil, 3H. 

9. One Pencil Eraser, E. Faber No. Ill, 

green ; One Sponge Eraser. 

10. Two Bottles Waterproof Drawing Ink, 

black and red. 

11. One Dozen thin edge Thumbtacks, }4>" 

diam. or less. 

12. One Penholder with Pens : Esterbrook & 

Co. Interstate, No. 815. 

13. One Transparent "French Curve." 



Note. — 'It is suggested, that no Ink Eraser or Knife be used for corrections in ink. 
green Pencil Eraser with the application of a little powdered Pumice will do neater work. 
Equipment not available in local stores can be ordered from the publishers. 



The 



VII 



EXPLANATORY NOTES 

The following sixty-five pages represent a set of sixty practical plates for Geometrical or Ele- 
mentary Mechanical Drawing for Secondary and Primary Schools. From these the instructor or 
student is to select a number of plates according to requirement or taste. A set of twenty-five 
plates is suggested as equivalent to a school year's work with one daily period or forty-five minutes, 
or to half a j'ear's work with double periods daily. The consecutive number of each chosen plate 
may be inserted in the space provided for. 

The size of each plate which the student is to make from the small sample drawing, is 
assumed to be 12" x 17", and good cream colored or white drawing paper should be used; the 
margin, represented by a heavy line, allows a space of one inch on each side. Each sample 
plate in this book has been furnished with dimensions measuring from the margin line, which 
will place the problems well on the sheet. The student observes, how a drawing might prop- 
erly be provided with dimensions ; yet, he is asked to omit the same from his plate, since this is a 
feature of Mechanical Drawing proper and not included in the present course. 

The sample plates are drawn "to scale," but at a reduced size; therefore the student will find 
it impossible, simpl)' to measure off from the sample any dimension with the dividers. In case 
a dimension should not readily be found on the plate, the student will have to compute or to 
calculate by proportion the desired length. 

A possible objection, that the student is merely "copying" a plate is not justified; he is repro- 
ducing a drawing of his own, using a good and correct sample, and since "Mechanical" Drawing 
requires a number of mechanical tools and skill in using them, it might well be said, that in 



VIII 



the elementary work of this sort emphasis be laid on the acquaintance with these tools and with 
their possibilities. The process of making a Mechanical Drawing in regard to forming a habit 
of good line work must become an unconscious, a mechanical one by repeated practice, before the 
student can pay all attention to advanced problems of design and construction. 

Neat lettering should receive special attention, and each plate should be valued in regard 
to careful lettering as well as to its line work; special "lettering plates," a practice in Free- 
hand printing, should be made from time to time. 

It is essential for the development of carefulness and skill to use ink after the plate has 
been completed in pencil ; waterproof black ink is recommended for the heavy lines, and red ink 
for the fine construction lines. If a variety of colored inks is preferred, there should be a uni- 
form system carried on throughout the whole course. 

Individual taste can well be taken into consideration, and changes on the suggested plates 
be made accordingly. 

Explanation of signs: R=Radius; Z-^Angle; ||^Parallel; _|_==Vertical. 
Pages 1, 2, 3, and 4 offer exercises in simple line work with the T-square and both triangles. 
Page 5 condenses the practice of several previous pages into one plate. 
Pages 6 and 7 contain simple straight line designs, which might also be used for practice in 

flat tinting. ; 

Page 8 shows block letters, filled in with black ink ; but any water color could be used instead. 
Pages 9, 10, 11, 12, 13, 14, 15, 16, and 17 introduce the use of the compass, circles alone or in 

connection with straight lines. 
Pages 18, 19, 20, 21, 22, and 23 deal with problems of Geometry. 



IX 



Page 18: Each Radius (R) on this page is arbitrary in length. Line A-B of the fourth prob- 
lem is drawn at any angle and of any length ; beginning at A, seven equal parts of any size 
are measured off on this line ; the last point is connected with C, and parallel lines to this 
drawn through each point towards A. 

Page 19 : In order to solve the sixth problem, A-B is bisected in C, an arc is drawn to E with 
R^C-D, and another arc with R=D-E to find F. D-F is equal to one side of the Pen- 
tagon. 

Page 21 : In the first problem bisect P-C in A; draw a circle with A as center and a Radius^ 
A-C and mark the points of intersection with the given circle. Connecting P with these 
points will furnish the tangents. 

In the second problem bisect A-B in C ; the arc with A-C as Radius intersects the arcs 
with Radius of B plus or minus Radius of A in point D. A parallel line to A-D at a dis- 
tance equal to Radius of A will locate the two points of tangency. 

In the third problem draw arcs around A with a Radius^R of A plus R of C and 
around B with a Radius^ R of B plus R of C, and find center for C at intersection. 

Problems four and five are Eolved by adding to or subtracting from line P-C the Radius 
of B. The bisecting perpendicular of P-B will meet the production of P-C in D, the cen- 
ter for the required circle. 

In the sixth problem draw arcs with R=A-C as shown, connect D with C, which inter- 
sects the perpendicular of A-C in E ; measure off the distance of A-C, beginning in E, 
three times and find H. H-B is equal to one-half of the circumference. 

Page 24 contains simple circle designs, applying problem four on page 18 and problem six on page 
19. 



Pages 25, 26, 27, and 28 show different designs for flat tinting in one or in different colors. 
Only first-class water colors and good brushes should be used. The sections of Standard 
Profile Steel on page 28 are taken from the catalog of Jones & Laughlin, Steel Company, 
Pittsburg. The pounds (fb) indicated, refer to weight of steel per foot. 

Page 29 includes compass curves and an exercise in "French" curves. 

Pages 30 and 31, showing the Spiral, Involute, and Volute, are drawn with the compass. The 
Spiral on the right side of page 30, however, is also drawn with the "French" curve. The In- 
volute is obtained by drawing arcs with Radii from 1, 2, 3, 4, etc., on the circumference 
of the given circle, to the tangent of each corresponding point. The Involute is applied in 
Gearing; the Volute is an architectural ornament. 

Pages 32, 33, and 34, showing curves formed by straight lines, are suggested as introduction to 
the curves proper. 

Page 35 presents methods to obtain a Parabola and a Hyperbola. 

Pages 36, ZT , and 38 are devoted to the Ellipse. The "Trammel," cut out from paper, on page 
36 moves with its two given points on C-D and A-B respectively, thus outlining at its outer 
end the Ellipse. The "Focus" of the Ellipse on page 38 is found by an arc with a Radius;^ 
one-half of the Major Axis. With one Focus as center and any Radius larger than the 
distance from the Focus to the nearest end of the Major Axis (in this case 1" has been 
chosen) draw an arc; with the other Focus as center and a Radius=Major Axis minus 
the chosen Radius of the first arc (1") draw another arc; both arcs will interect and lo- 
cate two points for the Ellipse; repeat this process any number of times with new dimen- 
sions. The second problem on page 38 is suggested as an example for drawing a Circle 



XI 



in Isometric Projection, where it becomes an Ellipse. Draw Square within Circle first, 
then 30° line with divisions as shown. The distance marked X is obtained with the divider 
from the circle construction and measured down from the 30° line for the Ellipse. 

Pages 39, 40, and 41 contain the three Conic Sections, which will produce the Hyperbola, the 
Parabola, and the Ellipse. The angles of 45° and 60° have been chosen for the sake of 
convenience and do not necessarily have to be of this size. 

Pages 42, 43, 44, and 45 show examples of the Cycloid, the Epicycloid, and the Hypocycloid. 
These curves are traces of a point on a circle rolhng on a straight line or on another circle. 
The equal distances marked 1, 2, 3, 4, etc., on the given circle, which is drawn first, are 
measured off from both sides of its center line on the straight line or the circle, on which 
the first circle is to roll. 

C}xloids are frequently used in Gearing. 

Page 46 represents the Helix, a curve, which resembles the path of a point uniformly moving 
around on the circumference of a cylinder and at the same time on the surface of the 
cylinder along a line parallel to its axis. The vertical distance, which is the point has 
moved along this line, is called the "Pitch"; Pitch and circumference of the Cylinder must 
always be drawn first to determine the points of construction for the Helix, and both are 
divided into the same number of equal parts. In order to save space, only one-half of the cir- 
cumference of the Cylinder is shown in each case. 

Pages 47 and 48 give examples of the Helix as a curve of different screw-threads. The very 
ends at the turn of each curve are best drawn with a compass, being too small for the 
"French" curves. 

Page 49 shows a symmetrical arrangement of "French" curves. 
Page 50 gives the construction of a truly Egg shaped Oval. 



XII 



Pages 51 and 52 submit a practical application of the Ellipse with a Major Axis of 29 and a 

Minor Axis of 18 feet. This Ellipse should be constructed first followed bjf the 23" divisions, 

beginning at each end of the curve towards the middle, and tangent to an arc drawn at each 

division point with a Radius of 24" is drawn the second and outer Ellipse. The slanting 
- lines- — between these two curves — 'are drawn from the point of tangency to the division 

point on the inner Ellipse. Note the use of a Scale: ^"^1 foot, which will be found on 

each triangular Architect's Scale. 
Pages 53 and 54 are dealing with problems to locate the path of motion of a point, which will 

be found to travel on an irregular curve, returning to its starting point. 
Page 55 shows examples in Shading. Note that with a darker tone of shadow the shading lines 

become narrower and heavier. 
Page 56 contains in outlines three important cases of Projection. Since this topic is treated 

largely in the second part of this work called "Descriptive Geometry," no further details 

or applications are given here. 
Pages 57, 58, 59, 60, 61 and 62 give three samples of Gothic design. The sheets showing the 

construction method in each ease, will furnish sufficient explanation. 
Page 63 shows a Balustrade with an application of plain surface shading. Note the Scale: 

lyi"^! Foot, found on the triangular Architect's Scale. • 
Pages 64 and 65 suggest an alphabet of shaded letters. Instead of the black shadow each letter 

might receive a light coat of water-color and the shaded part of it be painted in a darker 

tone of the same color. 
Page 66 contains some geometrical data, which might be convenient when computing various 

dimensions for geometrical figures. 




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A/o/e ■• Om// d/mens/ons o/-7c/ consfrc/cf/on/Znes. 



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A/o/e ■ Or?^/f c/zmens/ons . Use 2 or more e/zf/erer?/ co/ors. 



PLATEAUX 



Des/'gn fo^ f/a/ y/nf/nff . 




l\/ofe: Omi'f dimensions 



PLATE 




'\/ofe: Omit dir-nens/ons, bcjf /orof/'c/e pr/ntrriff. &rre cross secfions a //at finf of 1 1 g ht blue.. 






29 



To connect any nt/mber of po/'nts Cin this case 7 J tv/tf? compass curyes 
The giren dimensions /oca fe the points. 



-2i 



r^. 



Ctntre for /? C /^"iJ/Ws) is found of 

ir?/er'secf/or> of perpendicv/ar /bisector between fivo 
/ooinfs and exfensior) fron^ previous centre through 

nearest point 



-H 



Prtaref/'c^ tn French curifes, 
^ocafe jooinfs of ct/rv^s accoft^/n^ to ptven €f/mensiof7S. 




Note : Proy/c/e co/7sfr</ch'on //nes />? tz/oper cfratr/ng ; om/f a// cffmens/ons. 




Nofe ■■ Omif d/mensions 



PLAT£\i:i 



31 



/r>yo/c/fe 



/on/'c Volute 




Nofe : Omif d/rrfens/ons, but proy/de constrc/cfion in fine red //nes^ pr/nf/n^ and nc/mera/s /rt 



PLATE 




32 






/Vofe ■■ Omif d/mens/ons, but proi^/c^e construct ion /n f/ne red lines; nume rats and pr/nt/ng 

/n b/ack . 



PLA T£ [ 



33 



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/Vote- Om/J d/merrs/ons, buf prof/de consfrc/ct/on /n //ne reef //nesj nc/mera/s erne/ pr/r? fin q 

/n b/ac A . 




A/ofe; Om/'f (y/mens/ons, iiuf prov/o/e consf-rucf/on in fine red iines, ncz/Tiera/s a/7cf pr/nf/ng 

/n b/ack ■ 



PLATE 




A/o/e ■■ Om/f cf/mens/ons, baf pro^/c^e cor?sfruc//on /n //ne red // nes 



PLAT£L 


1 






36 








j 




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y4B-a'co-s'. 



Vote : Orn/t cf/mens/onSj i>ut pror/de consfrc/cfion /n //ne reef //n es and pr/nf/ng /n b/ack ink . 




A/o/^e : Omrf d/'mer?s/ons , buf prot^/de co/7sfrucf/on /n J7r?e reef //nes^ nc/m ero/s in t/ack ink. 



PLA T£\ I 



38 



"ii^ 



f/Z/pse 




C/rc/e and E/ 1 ipse 

I^^-J- i — ~\ I 




Nofe . Omif d/mens/ons, bc/f prov/'c/e consfrccf/on /r? //ne red f/nes; numera/^ /'n i>/acf( /nk . 



PLATE 




/Vote: Or?^/f c//r?7er7SJo/^s , baf prov/d e con strucf/ort /'n fine red //nes. 



PLATE 




/\/ote : Omff c///ne ns/ons, t>(/f proi^/c/e con 5trc/cf/on /n f/ne red fines. 



PLATE \ 1 
























41 


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^ofe. 0/-r)if dimens/of-i^,bL>f'proy/e/e c or-rs /rc/c t ion in f/rte rec/ /ines. 



PLATE dl 



42 



C yc/ o / d. 




///usfrafion of a Cyc/o/c/ . 




Nofe : Orn'f cf'nner7s/or?s J but proy/de consfri/cf/or? of cyc/o/d /n JY/7e rec/. //nes and n</mefah 
/r? £>/acA /n^!- Of77/t coji s/ruct/on on ///(/straf/on o/ cyc/o/d. 



PLATE VL 


D 






















43 




Epicyc/oid. 








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A/ofe ■ Om/t dimensions^ t>L/f /oroy/c/e cor?str(/cfior) >n fine rec/ /ines ancf numera/s /rj b/ack inA. 



PLA T£ I 



44 



Hyp o cy c/o /c/ 




Racf/r of /ar^e crrjc/ 
smo// ivhee/s in no g/t^pn preport/on 
fo each other 



Radius o/ sma/f 
w/iee/ = ^ rad/us of 
/argre whee/. 



A/o/e: Omif c/irnens/ons , but pro^/c/e construction in fine red fines. 



PL A TE\ 



45 



fTpicyc/otd 








EfD/' - anc^ Hy/^ 


•30- Cyc/o/c/. 








\ 


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/Vote: Om/t c//rr?ens/on3, bet protf/cfe con strucfion in fine reef /r'nes 



PLATE 'CH 




Note : Om/f d/mens/onsj i3i/f proy/de consfrucf/on /n /me red //nes^ nt/mercr/s ir7 b/ack /n k 



/^i/17'^ri 



47 



He//x 




n 

J 



/Mofe : Om/'f c^/>T7er7s/ons^ but proif/cfe constrccfion in fine red //nes ancf numera/s /n i>/acf( infs. 



PLA TE I I 



48 



■5yc/are Screir Threaa 




A/ofe- Om/f cf/mens/ons , tyc/f prov/'cfe construcffon m fine red /I'nes one/ numera/s in i>/ack 



I 



PLATE \I3 




A/o/e : Om/t d/mens/ons , t/ut prof/cfe cor/struct ion /n f/ne red //nes For con^struc t/or? 
e//y/c/e rcrc//'us /n/^o Z arye/ c frcarr?/ere'r7ce //-?fo ZZ e<yc/a/ parfs. 




Note: Om/f d/mens/on^ i'uf proi^/i/e pr/rrf/rrff . 



PLAT£\ 




Pracf'i'c a/ App//ca ^/on of /he ^///pse . 
( cor73/^rc>cf/on) 




A/o/ff -• On-7/f d/'mens/ons ana/ cor? street ion //neSj see /o//oyv/ng pcrye. 
Use Jca/e ■■ § "= / Fbtff. 



Note : // c/es/ree/, g/i^e br/dge cr //a f f/r?/ o/ //ph^ ^roy co/or 




A/o/e : Om/f c/imen s/ onSj i>cf ^roi^/de consfrccf/on /n reef /ines 



PLATEX 




Pof/i of mof/or? of po/nt D during one reyo/uti on of S oracinc/ centre C. 
/^o/nf A n^oyes r/'^hf crn of /ef/ on cf strcr/ghf iine. 



/Vo/e : Omi'f d/nnef-js/ons, but pro k'/aie con/sfrucf/'on /n //ne reef //nes. 



PLATE 




A/o/'e ■ Or?^ / /- cZ/m ^/7 3 /or? s 5hacy/ng //ries /n b/ack /'nk 



PLATEHIl 



56 



Project /on s. 



Ho/Zoyy Cube. 
2" S^cfare, tver//s ^" fh/cJc. 





Oi'/igc/e Pr o /ecf/'on 

On Z of J Axes -hor/zonfcrf 
C7r7d vef'f/ c Gr/~ df'rTnenstons 
are rfneasurecf fo// s/'zej 
or} fhe ffi/rc/ ox/s ~-4S "— 
the c//rrje ns forfs are hcjff 
size. 



/somefr/c Projecf/on 

On a// three A-^e3 - or? e ^fer/ica/ 
the other fivo at 30° to the hori- 
zon tat tin e — a// (/imens/ons 
crre rrt e a surety fott Size. 



on fa I f^rojecfior ffca view) 



lltrl/t<7/ f^rojeclrorj /"Jron^ v/et*} 



Orttio ctrapti/c Projection 
Atl yi'etrs of/tie' otject 
are proJeete</ yerti'cc/tty 
from one I'nto the other 
Oi'rnens/ons crre mecrsi/rect 
J'ott Size. 



A/o/'e- Proy/We a// exp/crrycrfory pr/n^/rtgr . 



PLATE\ 




Vote ■ Om/f d/mensfo ns ar7c/ con sfrucf^/o n fines- see /o//oiv/rtq page 



PLAT£\ 




A/o/e : // c/es/rea', //>?/ ^/oss pcrrf /n //gfhf b/ue, wood in i>rotvn co/or. 



PLATE \ 1 




— 






















59 




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Npfe: Omit d/mens/on s and constri/c/'on lines, see /o//oi^/nff pc/^e. 



PLAT£:{ 




4 



PLATE\ 




Note: Om/t c//nnens/ ons Cfr7ct cor7strucf-/or? //rresj see /o// o tvi ng page 



PLA TE EH 




A/ofe ■■ // des/red^ /'/nf g/assparf /n /I'^hf^ b/ue , i/vooc/ /n bro/yn co/or. 



PLATE\ I 



63 



S 



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t: 



A 



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"V 



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N 



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-2-6-^ 



f " 

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Cross ■Sec/-/ on ofA-B. 



Note : Om/f dim e/is/or> s ; proi'/c/e cross secf/or? /ines cfs s/iowr?. Use sca/e: /J"= /Foot. 



yOL/i/rnn 



64 




A/o/^e : Omif c//men5/ons ana/ corjsfracf/ on //nes ; sef fp/Zoiv/ng paffe. 



PLATE \ 



HIJKLHN 
OPOi 

¥W 



A/o/e .■ // des/recf ^/><? /e/^ers a //a/ f/nf, //ye blacM part a e/ar/rer /one 



66 







Po/ygo/i an 


a C/rcle 




mo/ 

»/ 
Po/y- 
9on 




0/art7 of 
Ctrc/e 


Lengfh o/ J I'cfe 
Po/rgon . 


O/a/m. of 

/nscritieei 

C/rc/e 


t: 


S/de D/ 


Ota m of 

CircumJC r. 

C/rc/e 


Area 
/^o/ygon 


Oicrrn 0/ 

c/r-curyns'cr 

C/rc/e 


3 


0.8 6 60 


/./ S47 


>> 0.4 330 


z. 


^ 


0. 707 1 


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■'5 


^'■ 


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o 


% 0.S878 


^ /.70/3 


\/. 7 205 


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6 


v, sooo 


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^ Z S98I 


%./. / S47 


7 


\ 0.438/ 


\ Z.30ZR 


% 3. 6 339 


t/./ 039 


6 


^ 0.i827 


5 Z. 6/37 


\ 4.8Za4 


\ /. 824 


£> 


\0.3 4Z0 


12. S 233 


I 6. / 8/8 


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^ 3.Z36/ 


< 7 694Z 


\ / OS/ s 


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C /. 04 2Z 


/2 


"^ Z S88 


\ 3 8 637 


'^/r IS62 


% / 033-3 

> 


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\ 0Z333 


i4. /786 


> /J / 8S6 


\./ 0Z9 9 


/4 


» ZZZS 


\4.^340 


-^I5.334S 


\ /.02s 7 


/J 


I O.Z 079 


\ 4. 6 097 


^/7 64 24 


\ /. 02 23 


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Q 0. / 9S/ 


\S. / ZS6 


Izo. / 094 


Z /. / 96 


/7 


10/8 38 


'ks. 44ZZ 


''22.73 SS 


-^/.0/73 


/d 


'i. 0/73 6 


\S. 7S88 


Xzsszoa 


^ /. /S4 


/J? 


■S: 1 6 46 


\6. 7SS 


>,284 6 SZ 


^ /.O / 38 


20 


^ /S64 


^ 6.39ZS 


^3/.S688 


^ /.O/ Z3 



Ceome/r/ca/ Oafa 

C/rcu/-r7/ere/7ce a/nc/ Areas o/C/rc/es 



To find C/rcumference m(y/ffp/y O/arrt.by 3./4/6 



To find Area mv/tip/y s^fc/are 0/ O/am.by .7gS4 



Tai)/e 0/ Dscima/ E-gu/ya/en/s 0/ ff" //[£"& ^". 



8/hs. 



i = IZS 



J =.2S 



4 =.so 



.%=.62S 



JS 



i = .87S 



? 



/6//15. 



h =-3'zs 



■.437S 



,fi ^.S6ZS 
fi -68 7S 



=.93 7S 



32tK/s. 



i, =.031 ZS- 



jz =09373- 



f. =./S6ZS 



■■.2/87S 



=.Z8/ZS 



V, =,3437S 



. =.406Z5r 



-.4 687S 



H =.S937S 



=.SS6ZS 



-.7/873- 



J5 =.73/ ZS 
fi -.8437^ 



ji =.96S7S 



6^/hs 



^=.0/S6SJ 



--.046875 



.078/23 



=./ 09373 



, ^.z-f-oezs 



M=.2 03/Z5 



=234373 



--.3SS37S 



#5 =390623 



if =433/23 



i^ =.<a4J75 



a =.3/3SZS 



'.54 6873 



=.S78/Z3 



■■.609373 



,640623 



\=.6 7/873 



il- 
64- 



.7.03/Z5 



?# =765625 



-.796875 



= 828/25 



if - 
64 



.859375 



=.S9 6ZS 



J:^ =.953/25 
S =.984375 



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Neutralizing agent: Magnesium Oxide 
Treatment Date: Oct. 2003 

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